Factor the following expression: $-5$ $x^2+$ $18$ $x$ $-16$
Solution: This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(-5)}{(-16)} &=& 80 \\ {a} + {b} &=& & & {18} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $80$ and add them together. The factors that add up to ${18}$ will be your ${a}$ and ${b}$ When ${a}$ is ${8}$ and ${b}$ is ${10}$ $ \begin{eqnarray} {ab} &=& ({8})({10}) &=& 80 \\ {a} + {b} &=& {8} + {10} &=& 18 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {-5}x^2 +{8}x +{10}x {-16} $ Group the terms so that there is a common factor in each group: $ ({-5}x^2 +{8}x) + ({10}x {-16}) $ Factor out the common factors: $ x(-5x + 8) - 2(-5x + 8) $ Notice how $(-5x + 8)$ has become a common factor. Factor this out to find the answer. $(-5x + 8)(x - 2)$